Nope, that's not right. Since we're talking about a resistive load, I can make the simplification that Power=Volts times Amps (and Power is proportional to Dollars).
We know that V = I*R. Since V is constant (120v RMS), we can only change the current in a circuit.
Undimmed the Light provides a resistance RL on the circuit.
Dimmed the Light plus dimmer (assuming a resistive dimmer, some are choppers, but I'm ignoring that now) provides a resistance RL+RD on the circuit.
So Undimmed the current, IL, is V/RL
Dimmed the current, ID, is V/(RL+RD)
That means that ID is less than IL and if the Power is V*I, then PD=V*ID is less than PL=V*IL. So less power is being consumed.